The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Carreira-Perpiñán, M. Á., Dayan, P., & Goodhill, G. J. (2005). Differential priors for elastic nets. In Lecture Notes in Computer Science (Vol. 3578, pp. 335–342). Springer Verlag. https://doi.org/10.1007/11508069_44
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